Talk:179: e to the pi times i

This is one of the few comics that were changed after release, as stated by Randall in his XKCD book. It first claimed e^(i*Pi) = 1, which lead to huge protest from the community and a correction from Randall. --Gefrierbrand (talk) 09:47, 3 September 2012 (UTC)

He must have been pie-eyed when he wrote that; he's usually pretty good about his math... -- IronyChef (talk) 05:09, 7 November 2012 (UTC)

I see what you did there. Daddy (talk) 15:18, 28 April 2013 (UTC)

You know, Leonhard Euler was really the one who brought the use of the symbol π into the mathematical mainstream. However, he originally wrote π = 6.28..., the circumference of a circle with radius 1—a unit circle. It was only later that he switched to the half-circumference instead, giving us the π = 3.14... that we know today. Perhaps Munroe was simply paying tribute to Euler's original definition.

Funnily enough, that value is what we would call 2π today, which some of us would denote as the single letter τ (tau). However, this strip predates the work that would come to popularize that notation by over 3 years. Since that work did come out, xkcd has had multiple strips directly referencing τ. I can't get a clear read on Munroe's feelings about the topic, though. ISaveXKCDpapers (talk) 03:41, 4 March 2025 (UTC)

What's is the difference between (6.28...)*radius and (3.14...)*diameter? 172.70.85.4 07:55, 4 March 2025 (UTC)

The difference of the quantities themselves is zero. As in, if you subtract the first from the second, the result you will get is 0. If you're talking about the conceptual difference between the representations of the quantities, there's a lot more that can be said about that. The short version is that in math, a circle's radius is usually thought of as more relevant than its diameter, including in the definition of what a circle is (the set of points in the plane that are a given distance from a given center). So in many situations, one can consider it clearer and more convenient to choose the radius-based number. However, others argue that the choice doesn't matter, and the diameter-based one is the traditional one, so we might as well stick with it. If you still want more, Wikipedia has a summary of the whole situation. But remember, I'm just giving the short version, so that's all I have to say. ISaveXKCDpapers (talk) 10:38, 15 April 2025 (UTC)

Randall says in the title text that he's never been satisfied with explanations of the sinusoidal nature of the function of e^ix. http://www.math.toronto.edu/mathnet/questionCorner/epii.html really helps, at least for those who are obsessed with taylor series yet tragically horrible at math. --Jolbucley (talk) 03:39, 29 January 2014 (UTC)

Why e to the ix gives a sinusoidal wave? This is because neutrinos keep oscillating. They wouldn't without the e^ix support... 162.158.83.72 04:01, 24 May 2016 (UTC)

Actually, e to the ix isn't sinusoidal. "Consisting of sinusoidal components" doesn't make it sinusoidal, any more than it does for any relation representable by Fourier Transform. As with the other mistake, it seems to indicate that this really wasn't something Randall knew about.

Technically i isn't "imaginary" at all, but is incorporated into equations to represent rotations perpendicular to the x-y plane. 108.162.210.220 15:51, 9 September 2016 (UTC)

i is imaginary. Both "real" and "imaginary" are terms of art in a mathematical context that have nothing to do with the reality or unreality of the numbers in question. Also, when you're talking about the complex plane, it doesn't have x and y axes: it has real and imaginary axes. But of course, nobody can stop you from defining a mapping from the complex plane to any other vector space if that suits your purpose. 162.158.62.45 01:58, 6 September 2018 (UTC)